Finite Group Databasebeta

← #25259917

Subgroups — #25259917

Order 11008.

2586 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2#19137739C214yesmaximal, complemented
3#19137609C212yesmaximal, complemented
4#19137598C212yesmaximal, complemented
5#19137537C212yesmaximal, complemented
6#19137499C212yesmaximal, complemented
7#19137486C211yesmaximal, characteristic, complemented
8#19137478C211yesmaximal, characteristic, complemented
9#19137435C211yesmaximal, characteristic, complemented
10#19137426C211yesmaximal, characteristic, complemented
11#19137288C212yesmaximal, complemented
12#19137277C212yesmaximal, complemented
13#19137250C214yesmaximal, complemented
14#19137235C212yesmaximal, complemented
15#19137224C212yesmaximal, complemented
16C2×#14582759C211yesmaximal, characteristic, complemented
17C43×#2280C211yesmaximal, characteristic, complemented
18C22×#10621898C2211yescharacteristic
19#14583410C4116yescomplemented
20C2×#13063308C2212yes—
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×#13063294C2212yes—
26C2×C4×Dic86C2212yescomplemented
27C2×C4×D172C2212yescomplemented
28C2×C4×C22⋊D43C2212yes—
29C2×C4×C22⋊D43C2212yes—
30C2×(C22⋊D43)⋊C4C2214yes—
31C2×#13063284C2211yescharacteristic
32C22×C4⋊Dic43C2212yes—
33C22×C22⋊Dic43C2212yes—
34#14582805C2212yescomplemented
35#14582801C2212yescomplemented
36#14582799C2214yes—
37#14582799C2214yes—
38#14582797C2212yescomplemented
39#14582797C2212yescomplemented
40#14582796C2214yescomplemented
41#14582794C2214yescomplemented
42#14582793C2214yes—
43#14582793C2214yes—
44#14582791C2214yescomplemented
45#14582789C2214yescomplemented
46#14582787C2214yes—
47#14582787C2214yes—
48#14582786C2214yescomplemented
49#14582780C2214yescomplemented
50#14582776C2214yes—
51#14582775C2214yes—
52#14582775C2214yes—
53#14582773C2214yescomplemented
54#14582771C2214yes—
55#14582770C2214yescomplemented
56#14582766C2212yescomplemented
57#14582763C2212yescomplemented
58#14582761C2212yescomplemented
59#14582759C2212yes—
60#14582759C2211yescharacteristic
61#14582759C2211yescharacteristic
62#14582759C2212yes—
63#14582759C2212yes—
64#14582758C2212yescomplemented
65C4×C4⋊Dic43C2212yescomplemented
66C4×C4⋊Dic43C2212yescomplemented
67#14582750C2212yescomplemented
68C22⋊C4×Dic43C2214yes—
69#14582746C2212yescomplemented
70#14582744C2212yescomplemented
71C2×C43⋊#95C2212yes—
72#95×D43C2212yescomplemented
73C24×C4×C43C2211yescharacteristic
74C2×#117×C43C2212yes—
75C43×#381C2211yescharacteristic
76C43×#381C2211yescharacteristic
77C43×#380C2211yescharacteristic
78C43×#380C2212yes—
79C43×#380C2211yescharacteristic
80C43×#379C2212yes—
81C4×C22⋊C4×C43C2212yes—
82C4×C22⋊C4×C43C2211yescharacteristic
83C4×C22⋊C4×C43C2211yescharacteristic
84C2×#10621898—44no—
85C2×#10621898C2×C418yescomplemented
86C22×Dic86C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×C22⋊D43C2312yes—
89C22×C22⋊D43C2312yes—
90C22×C22⋊D43C2312yes—
91C23×Dic43C2314yes—
92C22×C4×D43C2314yes—
93C22×C4×D43C2312yes—
94#13063308C2×C4116yescomplemented
95#13063304C2×C418yescomplemented
96#13063304C2×C418yescomplemented
97#13063299C2×C418yes—
98#13063299C2×C418yescomplemented
99#13063294C2×C4116yescomplemented
100C4×Dic86—44no—
101C4×D172—44no—
102C4×C22⋊D43C2×C4116yescomplemented
103C4×C22⋊D43C2×C4116yescomplemented
104(C22⋊D43)⋊C4—48no—
105#13063284C2×C418yescomplemented
106C2×C4⋊Dic43—44no—
107C2×C4⋊Dic43C2312yes—
108C2×C4⋊Dic43C2312yes—
109C2×C4⋊Dic43C2314yes—
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4C2314yes—
113C2×Dic43⋊C4C2314yes—
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2312yes—
116C2×Dic43⋊C4C2312yes—
117C2×C22⋊Dic43—44no—
118C2×C22⋊Dic43C2312yes—
119C2×C22⋊Dic43C2314yes—
120C2×C22⋊Dic43C2312yes—
121C2×C22⋊Dic43C2312yes—
122C2×C22⋊Dic43C2312yes—
123C2×C22⋊Dic43C2312yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×(C2×D43)⋊C4C2312yes—
128C2×(C2×D43)⋊C4C2312yes—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2312yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C43⋊#95C2314yes—
140C43⋊#95C2312yes—
141C43⋊#95C2312yes—
142C25×C43C2311yescharacteristic
143C23×C4×C43—44no—
144C23×C4×C43C2×C418yescomplemented
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151#117×C43—44no—
152C2×C4⋊C4×C43C2312yes—
153C2×C4⋊C4×C43C2312yes—
154C2×C22⋊C4×C43C2312yes—
155C2×C22⋊C4×C43C2312yes—
156C2×C22⋊C4×C43C2312yes—
157C2×C22⋊C4×C43C2312yes—
158C2×C22⋊C4×C43C2312yes—
159C2×C22⋊C4×C43C2312yes—
160C2×C42×C43C2312yes—
161C2×C42×C43C2312yes—
162#95×C43C2312yes—
163#95×C43C2312yes—
164#95×C43C2311yescharacteristic
165#95×C43C2311yescharacteristic
166#95×C43C2311yescharacteristic
167#95×C43C2311yescharacteristic
168C24×C43—22no—
169C24×C43—22no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43C22×C414yes—
173C24×C43C2411yescharacteristic
174C24×C43C2411yescharacteristic
175C24×C43C2411yescharacteristic
176C23×D43C2412yes—
177C22×C4×C43—24no—
178C22×C4×C43—24no—
179C22×C4×C43—24no—
180C22×C4×C43—42no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43—416no—
184C22×C4×C43C22×C414yes—
185C22×C4×C43C22×C414yes—
186C22×C4×C43C22×C414yes—
187C22×C4×C43C22×C414yes—
188C22×C4×C43C22×C414yes—
189C22×C4×C43C22×C414yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—44no—
201C2×C22⋊D43—44no—
202C2×C22⋊D43C22×C418yes—
203C2×C22⋊D43C22×C418yes—
204C2×C22⋊D43C22×C418yes—
205C22×Dic43—28no—
206C22×Dic43—44no—
207C22×Dic43—44no—
208C22×Dic43C2414yes—
209C22×Dic43C2414yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213#10621898—416no—
214C2×D172—24no—
215C2×D172C22×C414yes—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×C4×D43—44no—
219C2×C4×D43—44no—
220C2×C4×D43C22×C418yes—
221C2×Dic86—24no—
222C2×Dic86C22×C414yes—
223C4⋊C4×C43—42no—
224C4⋊C4×C43—42no—
225C22⋊C4×C43—24no—
226C22⋊C4×C43—24no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C42×C43—24no—
232C42×C43—24no—
233C22⋊Dic43—42no—
234C22⋊Dic43—44no—
235C22⋊Dic43—42no—
236C22⋊Dic43C22×C418yes—
237C22⋊Dic43C22×C418yes—
238C22⋊Dic43C22×C418yes—
239(C2×D43)⋊C4—44no—
240(C2×D43)⋊C4—44no—
241(C2×D43)⋊C4—44no—
242(C2×D43)⋊C4C22×C418yes—
243(C2×D43)⋊C4C22×C418yes—
244C4⋊Dic43—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43—44no—
247C4⋊Dic43C22×C414yes—
248C4⋊Dic43C22×C414yes—
249Dic43⋊C4—44no—
250Dic43⋊C4—44no—
251Dic43⋊C4—44no—
252Dic43⋊C4C22×C418yes—
253Dic43⋊C4C22×C418yes—
254C4×Dic43—44no—
255C4×Dic43—44no—
256C4×Dic43—44no—
257C4×Dic43C22×C418yes—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—28no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—44no—
270C23×C43—44no—
271C23×C43—48no—
272C23×C43—48no—
273C23×C43C23×C412yes—
274C23×C43C23×C412yes—
275C23×C43C23×C412yes—
276C23×C43H(5,𝔽2)12yes—
277C23×C432−1+412yes—
278C23×C43C2511yescharacteristic
279C22×D43—22no—
280C22×D43—24no—
281C22×D43—22no—
282C22×D43—24no—
283C22×D43C23×C414yes—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—28no—
288C2×C4×C43—28no—
289C2×C4×C43—28no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—44no—
303C2×C4×C43—44no—
304C2×C4×C43—44no—
305C2×C4×C43C23×C412yes—
306C2×C4×C43C23×C412yes—
307C2×C4×C43C23×C412yes—
308C2×C4×C43C23×C412yes—
309C2×C4×C43H(5,𝔽2)14yes—
310C22⋊D43—216no—
311C22⋊D43—48no—
312C22⋊D43—48no—
313C2×Dic43—22no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—24no—
317C2×Dic43—24no—
318C2×Dic43—24no—
319C2×Dic43—24no—
320C2×Dic43—24no—
321C2×Dic43—24no—
322C2×Dic43—24no—
323C2×Dic43—88no—
324C2×Dic43C23×C414yes—
325C2×Dic43C23×C414yes—
326C2×Dic43C23×C414yes—
327D172—28no—
328C4×D43—48no—
329C4×D43—88no—
330Dic86—28no—
331#34404—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—24no—
335C22×C43—24no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—416no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43#52014yes—
348C22×C43C24×C411yescharacteristic
349C22×C43C2×H(5,𝔽2)12yes—
350C22×C43C2×H(5,𝔽2)11yescharacteristic
351C22×C43C2×2−1+411yescharacteristic
352C22×C43#58512yes—
353C2×D43—24no—
354C2×D43—24no—
355C2×D43—24no—
356C2×D43—44no—
357C2×D43—44no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43#51814yes—
366Dic43—24no—
367Dic43—24no—
368Dic43—24no—
369Dic43—44no—
370Dic43—44no—
371C2×#525—431no—
372#2376—434no—
373#2361—432no—
374#2360—432no—
375#2353—432no—
376#2349—432no—
377#2347—431no—
378#2346—431no—
379#2341—431no—
380#2339—431no—
381#2324—432no—
382#2323—432no—
383#2321—434no—
384#2319—432no—
385#2318—432no—
386#2280D4311yescharacteristic, complemented
387C2×#380—431no—
388C2×C43—24no—
389C2×C43—42no—
390C2×C43—42no—
391C2×C43C2×#51811yescharacteristic
392C2×C43C2×#52011yescharacteristic
393C2×C43#342811yescharacteristic
394C2×C43#354112yes—
395C2×C43#354212yes—
396D43—44no—
397C22×#41—431no—
398C24×C4C2×D4311yescharacteristic
399#525—4316no—
400C2×#123—432no—
401C2×C22⋊Q8—431no—
402C2×C22⋊Q8—431no—
403C2×#121—431no—
404C2×#121—431no—
405C2×#120—432no—
406C2×C4×Q8—432no—
407C2×C4×D4—432no—
408C2×C4×D4—432no—
409C2×C4×D4—434no—
410C2×C4×D4—432no—
411C2×#117—431no—
412C2×#117C2×D4312yes—
413C22×C4⋊C4—432no—
414C22×C22⋊C4—432no—
415#391—432no—
416#390—434no—
417#390—434no—
418#390—432no—
419#389—434no—
420#389—432no—
421#389—432no—
422#389—434no—
423#388—434no—
424#388—434no—
425#388—434no—
426#388—434no—
427#388—434no—
428#388—434no—
429#387—434no—
430#387—434no—
431#386—434no—
432#386—434no—
433#386—434no—
434#385—434no—
435#385—434no—
436#385—434no—
437#383—432no—
438#382—432no—
439#381—432no—
440#381C2×D4311yescharacteristic
441#381C2×D4311yescharacteristic
442#380—432no—
443#380—432no—
444#380—431no—
445#380—431no—
446#380—432no—
447#380—432no—
448#380C2×D4311yescharacteristic
449#380C2×D4311yescharacteristic
450#380C2×D4312yes—
451#379C2×D4312yes—
452C4×C4⋊C4—432no—
453C4×C4⋊C4—432no—
454C4×C4⋊C4—432no—
455C4×C22⋊C4—434no—
456C4×C22⋊C4—432no—
457C4×C22⋊C4C2×D4311yescharacteristic
458C4×C22⋊C4C2×D4311yescharacteristic
459C4×C22⋊C4C2×D4312yes—
460#376—432no—
461C2×#95—432no—
462C2×#95—432no—
463C43#3440411yescharacteristic, complemented, Sylow
464C25C22×D4311yescharacteristic
465C2×#41—438no—
466C2×#41—1724no—
467C22×Q8—431no—
468C22×D4—432no—
469C22×D4—432no—
470C22×D4—432no—
471C22×D4—431no—
472C23×C4—44no—
473C23×C4—432no—
474C23×C4—434no—
475C23×C4—434no—
476C23×C4C4×D4318yescomplemented
477C23×C4C22×D4311yescharacteristic
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483#123—4316no—
484C22⋊Q8—438no—
485C22⋊Q8—438no—
486#121—438no—
487#121—438no—
488#120—4316no—
489C4×Q8—1724no—
490C4×D4—4316no—
491C4×D4—4316no—
492C4×D4—1724no—
493C4×D4—1728no—
494#117—44no—
495#117—438no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—432no—
499C2×C4⋊C4—432no—
500C2×C4⋊C4—432no—
501C2×C4⋊C4—432no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—434no—
504C2×C4⋊C4—434no—
505C2×C4⋊C4—434no—
506C2×C4⋊C4—1724no—
507C2×C4⋊C4C22×D4312yes—
508C2×C4⋊C4C22×D4312yes—
509C2×C22⋊C4—432no—
510C2×C22⋊C4—432no—
511C2×C22⋊C4—432no—
512C2×C22⋊C4—432no—
513C2×C22⋊C4—432no—
514C2×C22⋊C4—432no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—432no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—1724no—
521C2×C22⋊C4C22×D4312yes—
522C2×C22⋊C4C22×D4312yes—
523C2×C22⋊C4C22×D4312yes—
524C2×C22⋊C4C22×D4312yes—
525C2×C22⋊C4C22×D4312yes—
526C2×C22⋊C4C22×D4312yes—
527C2×C42—432no—
528C2×C42—434no—
529C2×C42—434no—
530C2×C42—434no—
531C2×C42C22×D4312yes—
532C2×C42C22×D4312yes—
533#95—432no—
534#95—432no—
535#95—434no—
536#95—434no—
537#95—434no—
538#95—434no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95C22×D4311yescharacteristic
543#95C22×D4311yescharacteristic
544#95C22×D4311yescharacteristic
545#95C22×D4311yescharacteristic
546#95C22×D4312yes—
547#95C22×D4312yes—
548C24—22no—
549C24—22no—
550C24—42no—
551C24—42no—
552C24—432no—
553C24C2×C4×D4314yes—
554C24C23×D4311yescharacteristic
555C24C23×D4311yescharacteristic
556C24C23×D4311yescharacteristic
557#41—17216no—
558C2×Q8—434no—
559C2×Q8—864no—
560C2×D4—438no—
561C2×D4—438no—
562C2×D4—438no—
563C2×D4—434no—
564C2×D4—864no—
565C2×D4—864no—
566C2×D4—864no—
567C2×D4—1724no—
568C2×D4—1724no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—416no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—438no—
580C22×C4—434no—
581C22×C4—434no—
582C22×C4—868no—
583C22×C4—1724no—
584C22×C4—1724no—
585C22×C4—1724no—
586C22×C4—1724no—
587C22×C4—1724no—
588C22×C4—1724no—
589C22×C4C2×C4×D4314yes—
590C22×C4C2×C4×D4314yes—
591C22×C4C2×C4×D4314yes—
592C22×C4C2×C4×D4314yes—
593C22×C4C2×C4×D4314yes—
594C22×C4C2×C4×D4314yes—
595C22×C4C23×D4312yes—
596C22×C4C23×D4312yes—
597C22×C4C23×D4312yes—
598C22×C4C23×D4312yes—
599C22×C4C23×D4311yescharacteristic
600C22×C4C23×D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—434no—
606C4⋊C4—434no—
607C4⋊C4—438no—
608C4⋊C4—438no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—1724no—
612C4⋊C4—1724no—
613C4⋊C4—1724no—
614C4⋊C4—1724no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—438no—
622C22⋊C4—438no—
623C22⋊C4—438no—
624C22⋊C4—438no—
625C22⋊C4—438no—
626C22⋊C4—1724no—
627C22⋊C4—1724no—
628C22⋊C4—1724no—
629C22⋊C4—1722no—
630C22⋊C4—1724no—
631C22⋊C4—1722no—
632C42—24no—
633C42—24no—
634C42—438no—
635C42—1724no—
636C42—1724no—
637C42—1724no—
638C23—22no—
639C23—22no—
640C23—28no—
641C23—22no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—48no—
653C23—434no—
654C23—864no—
655C23—862no—
656C23—862no—
657C23—864no—
658C23C22×C4×D4312yes—
659C23C22×C4×D4312yes—
660C23C22×C4×D4312yes—
661C23#1306337112yes—
662C23#1306337212yes—
663C23C24×D4311yescharacteristic
664Q8—868no—
665D4—8616no—
666D4—868no—
667D4—1728no—
668D4—1728no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—434no—
691C2×C4—434no—
692C2×C4—434no—
693C2×C4—864no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—864no—
697C2×C4—864no—
698C2×C4—864no—
699C2×C4—864no—
700C2×C4—864no—
701C2×C4—864no—
702C2×C4—864no—
703C2×C4—3448no—
704C2×C4—3448no—
705C2×C4—1728no—
706C2×C4C22×C4×D4312yes—
707C2×C4C22×C4×D4312yes—
708C2×C4C22×C4×D4312yes—
709C2×C4C22×C4×D4312yes—
710C2×C4#1306337014yes—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—864no—
727C22—864no—
728C22—864no—
729C22—1724no—
730C22—1724no—
731C22#1458337914yes—
732C22C23×C4×D4311yescharacteristic
733C22C2×#1306337012yes—
734C22C2×#1306337111yescharacteristic
735C22C2×#1306337211yescharacteristic
736C22#1458373512yes—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—864no—
745C4—864no—
746C4—864no—
747C4—1724no—
748C4—1724no—
749C4#1458337214yes—
750C2—24no—
751C2—42no—
752C2—42no—
753C2—1724no—
754C2C2×#1458337211yescharacteristic
755C2C2×#1458337911yescharacteristic
756C2#1914779611yescharacteristic
757C2#1914888812yes—
758C2#1914891112yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2280C2
socle, cosocleC23×C43C25
prime radicalC2×#14583410C2
hypercenter#2280D43
hypocenterC43#34404
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2280

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19137739C2semidirect
3. #19137609C2semidirect
4. #19137598C2semidirect
5. #19137537C2semidirect
6. #19137499C2semidirect
7. #19137486C2semidirect
8. #19137478C2semidirect
9. #19137435C2semidirect
10. #19137426C2semidirect
11. #19137288C2semidirect
12. #19137277C2semidirect
13. #19137250C2semidirect
14. #19137235C2semidirect
15. #19137224C2semidirect
16. C2×#14582759C2semidirect
17. C43×#2280C2semidirect
19. #14583410C4semidirect
26. C2×C4×Dic86C22semidirect
27. C2×C4×D172C22semidirect
34. #14582805C22semidirect
35. #14582801C22semidirect
38. #14582797C22semidirect
39. #14582797C22semidirect
40. #14582796C22semidirect
41. #14582794C22semidirect
44. #14582791C22semidirect
45. #14582789C22semidirect
48. #14582786C22semidirect
49. #14582780C22semidirect
53. #14582773C22semidirect
55. #14582770C22semidirect
56. #14582766C22semidirect
57. #14582763C22semidirect
58. #14582761C22semidirect
64. #14582758C22semidirect
65. C4×C4⋊Dic43C22semidirect
66. C4×C4⋊Dic43C22semidirect
67. #14582750C22semidirect
69. #14582746C22semidirect
70. #14582744C22semidirect
72. #95×D43C22semidirect
85. C2×#10621898C2×C4semidirect
94. #13063308C2×C4semidirect
95. #13063304C2×C4semidirect
96. #13063304C2×C4semidirect
98. #13063299C2×C4semidirect
99. #13063294C2×C4semidirect
102. C4×C22⋊D43C2×C4semidirect
103. C4×C22⋊D43C2×C4semidirect
105. #13063284C2×C4semidirect
144. C23×C4×C43C2×C4semidirect
386. #2280D43semidirect
463. C43#34404semidirect
476. C23×C4C4×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145834102
#191377392
#191376092
#191375982
#191375372
#191374992
#191374862
#191374782
#191374352
#191374262
#191372882
#191372772
#191372502
#191372352
#191372242
C2×#145827592
C43×#22802
#3440443